Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential

Details Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential

2004-05-21

arxiv.org/abs/math/0405411v1

Commun. Contemp. Math., Vol. 7, No. 4 (2005) 483-508

Mathematics

Analysis of PDEs

20 pages; survey of previous results

Scientific paper

10.1142/S0219199705001829

We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and the nonlinear effects, can be described quite precisely. This includes semi-classical regimes, as well as finite time blow-up and scattering issues. We present the tools used for these problems, as well as their limitations, and outline the arguments of the proofs.

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